The eta transition form factor from space- and time-like experimental data

TL;DR

This paper analyzes the eta transition form factor in both space- and time-like regions using a model-independent approach, providing precise parameters and exploring implications for eta-eta' mixing and radiative decays.

Contribution

It introduces a model-independent analysis of the eta transition form factor across regions, extracting precise parameters and examining their impact on mixing and decay processes.

Findings

Most precise slope and curvature parameters obtained

Values at zero and infinity determined accurately

Implications for eta-eta' mixing and radiative decays discussed

Abstract

The $\eta$ transition form factor is analysed for the first time in both space- and time-like regions at low and intermediate energies in a model-independent approach through the use of rational approximants. The $\eta\rightarrow e^+e^-\gamma$ experimental data provided by the A2 Collaboration in the very low energy region of the dilelectron invariant mass distribution allows for the extraction of the most precise up-to-date slope and curvature parameters of the form factors as well as their values at zero and infinity. The impact of these new results on the mixing parameters of the $\eta$-$\eta^\prime$ system, together with the role played by renormalisation dependent effects, and on the determination of the $VP\gamma$ couplings from $V\to P\gamma$ and $P\to V\gamma$ radiative decays are also discussed.